Markovian properties of passive scalar increments in gridgenerated turbulence
Abstract
Recent research (Renner, Peinke and Friedrich 2001 J. Fluid Mech. 433 383) has shown that the statistics of velocity increments in a turbulent jet exhibit Markovian properties for scales of size greater than the Taylor microscale, lgr. In addition, it was shown that the probability density functions (PDFs) of the velocity increments, v (r), were governed by a FokkerPlanck equation. Such properties for passive scalar increments have never been tested. The present work studies the (velocity and) temperature field in gridgenerated wind tunnel turbulence for Taylormicroscalebased Reynolds numbers in the range 140lesR_{lgr}les582. Increments of longitudinal velocity were found to (i) exhibit Markovian properties for separations rgaplgr and (ii) be describable by a FokkerPlanck equation because terms in the KramersMoyal expansion of order >2 were small. Although the passive scalar increments, dgr(r), also exhibited Markovian properties for a similar range of scales as the velocity field, the higherorder terms in the KramersMoyal expansion were found to be nonnegligible at all Reynolds numbers, thus precluding the PDFs of dgr(r) from being described by a FokkerPlanck equation. Such a result indicates that the scalar field is less Markovian than the velocity field—an attribute presumably related to the higher level of internal intermittency associated with passive scalars.
 Publication:

New Journal of Physics
 Pub Date:
 May 2004
 DOI:
 10.1088/13672630/6/1/049
 Bibcode:
 2004NJPh....6...49T